Pigeon paradox reveals quantum cosmic connections

A thought experiment involving a paradox of pigeons shows a new kind of quantum link that could be happening everywhere in the cosmos, all the time

PARTICLES on opposite ends of the universe can link quantum mechanical hands. The phenomenon hints at an entirely new aspect of the quantum reality underlying all matter.

The effect is a sort of inversion of one of the most famous and profound quantum properties, called entanglement. Two entangled particles share a single quantum state: they behave as one and cannot be described individually. Measuring one instantaneously affects the other, no matter how far apart they become, an oddity that prompted Einstein to describe entanglement as "spooky action at a distance".

However, for this to happen the particles must have interacted in some way when they came into existence, which may mean only a small fraction of the particles in the universe are entangled at any given time. Cosmic connections make no such demands. "They have no interaction, they have no idea that the other particle even existed," says Jeff Tollaksen of Chapman University in Orange, California.

The effect is based on work by Yakir Aharonov, also at Chapman University, in the 1960s. He and his colleagues showed that, mathematically speaking, a system's properties can be influenced by measurements made in the future. Aharonov has been studying the strange consequences of this "post-selection" process ever since.

Now Aharonov, Tollaksen, Sandu Popescu and their colleagues show mathematically that post-selection should link any two particles every time their quantum properties are measured, no matter where they are in the universe. In other words, all particles everywhere could be linked, provided they have been post-selected in some way. "Is that mind-blowing or is that mind-blowing?" Tollaksen says.

Knowing that such an extraordinary claim would need to be backed up, the researchers devised a thought experiment to demonstrate the simplest case in which a cosmic correlation between two particles would be obvious and testable. The thought experiment, which the team calls the "quantum pigeonhole effect", reveals how quantum particles subvert the rules of regular mathematics.

Imagine you have to house three pigeons in two pigeonholes. In the classical world, it's obvious that at least two pigeons will have to share.

Swap your pigeons

But for quantum particles, this is not necessarily true. Swap your pigeons for electrons, and send them three at a time into an interferometer. This device splits each electron into two, sends them along both paths simultaneously, then brings them together again.

Then "post-select" some of the electrons to influence their past state. You do this by measuring the electrons' states when they exit the interferometer, selecting electrons in a particular state that is significantly different to the one they had when they entered. That should create quantum links between those electrons, Tollaksen says (see diagram).

To show the links are really there, you need to know what the electrons are doing inside the device. Another quantum effect, called superposition, means that each electron takes both paths at once. If any two of the three electrons share one arm, which must happen classically, their identical electrical charges will repel one another, deflecting their trajectories ever so slightly. That deflection should be detectable when the electrons exit the interferometer.

Because superposition is a delicate state, if you try to measure the path any electron took, it will pick a side and you will find it in one or the other. But if you check the paths of any pair of the three original electrons, the detector will show no deflection has happened. In other words, you can have three pigeons and two boxes, and yet no two pigeons are ever found in the same box. A linkage must exist, because it's as if the particles know the other is there, and avoid each other.

Furthermore, this works no matter how many pigeons you have. "You can put an infinite number of pigeons in two boxes, and no two pigeons will be in the same box," says Tollaksen (arxiv.org/abs/1407.3194).

The quantum pigeonhole effect is the simplest way to test the idea that unrelated particles can be correlated simply by being post-selected. You would only need to bring the particles together in the interferometer to test that they are in fact correlated. In theory, these electrons could be spread across the universe, never come anywhere near each other, and mere post-selection would link them up.

Given that this is happening to real particles all the time, either due to human measurements or natural interactions, does this mean that particles everywhere in the universe are correlated? "I'd say that the answer to that is yes," says Tollaksen.

This is a surprising breakthrough, says Paul Davies at Arizona State University in Tempe. "It's remarkable that it's still possible to discover something fundamentally new about quantum mechanics, which has been around for nearly 100 years," he says. "Here we see a richer, more complex set of long-range correlations that nobody knew existed before."

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